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Received August 2, 2020; Accepted September 11, 2020; Published September 28, 2020
Abstract. In this paper, we investigate the split equality common fixed-point problem of firmly quasi-nonexpansive operators in Hilbert spaces. We introduce new iterative algorithms with a way of selecting the step-sizes such that its implementation does not need any prior information about the operator norms. The new methods are extended from the method for solving the split common fixed-point problem. The range of the new step-sizes even can be enlarged two times. Under suitable conditions, we establish a weak convergence theorem of the proposed algorithm and a strong convergence theorem of its variant by the viscosity approximation method. Numerical results are reported to show the effectiveness of the proposed algorithm.
How to Cite this Article:
Jing Zhao, Yuan Li, Haili Zong, Improved self-adaptive iterative algorithms for the split equality common fixed-point problem of firmly quasi-nonexpansive operators, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 41, pp. 1-16.